The Caribbean is not near as good a deal for shopping as it was several years ago. Way too many ships visiting for the shop owners to be particularly hungry. Many of the islands have also become dominated by the larger chains buying out the smaller locations.
(You can see 7 Diamonds International in a 6 block stretch)
On the other hand the selection is very good with so many shops. Just KNOW your prices, and you MAY be able to do OK... but be prepared to walk away if they don't meet your price.